User interface language: English | Español

Date May 2022 Marks available 3 Reference code 22M.1.SL.TZ2.10
Level Standard Level Paper Paper 1 Time zone Time zone 2
Command term Find Question number 10 Adapted from N/A

Question

The masses of Fuji apples are normally distributed with a mean of 163g and a standard deviation of 6.83g.

When Fuji apples are picked, they are classified as small, medium, large or extra large depending on their mass. Large apples have a mass of between 172g and 183g.

Approximately 68% of Fuji apples have a mass within the medium-sized category, which is between k and 172g.

Determine the probability that a Fuji apple selected at random will be a large apple.

[2]
a.

Find the value of k.

[3]
b.

Markscheme

sketch of normal curve with shaded region to the right of the mean and correct values           (M1)

0.0921   0.0920950           A1

 

[2 marks]

a.

EITHER

Px<172

0.906200           (A1)


0.906200-0.68

0.226200           (A1)


OR

P163<x<172

0.406200           (A1)


0.5-0.68-0.406200   OR   0.5+0.68-0.406200

0.226200   OR   0.773799           (A1)


OR

           (A1)(A1)

 

Note: Award A1 for a normal distribution curve with a vertical line on each side of the mean and a correct probability of either 0.406 or 0.274 or 0.906 shown, A1 for a probability of 0.226 seen.


THEN

k= 158g  157.867g           A1

 

[3 marks]

b.

Examiners report

A straightforward calculation of probability for a normal distribution was well done.

a.

The majority of candidates used 0.68 as the area to the left of k. Very few candidates knew how to approach the question when the probability given was not the complete area to the left or right of k.

b.

Syllabus sections

Topic 4—Statistics and probability » SL 4.9—Normal distribution and calculations
Show 181 related questions
Topic 4—Statistics and probability

View options